System and method for determining a transfer of torque from the surface to a drill bit

ABSTRACT

A method for determining a total torque output at a drill bit includes receiving an on-bottom pressure and an off-bottom pressure. The method also includes determining a differential pressure based upon the on-bottom pressure and the off-bottom pressure. The method also includes receiving a surface torque. The method also includes determining a torque transmission coefficient based at least partially upon the differential pressure and the surface torque. The method also includes determining the total torque output at the drill bit based at least partially upon the differential pressure, the surface torque, and the torque transmission coefficient.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 63/268,879, filed on Mar. 4, 2022, the entirety of which isincorporated by reference herein.

BACKGROUND

Mud motors are part of a downhole assembly (also referred to as a bottomhole assembly or BHA) and are widely used for directional drilling andperformance drilling. A mud motor is used to transform hydraulic energyof the drilling fluid (e.g., mud) into mechanical energy on a rotatingshaft. More particularly, the mud motor transforms the hydraulic power,which is essentially the flow rate Q and the active differentialpressure ΔP_(a), into an output torque for the drill bit T andadditional bit rotation from the motor that may be called RPM_(m).

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

A method for determining a total torque output at a drill bit isdisclosed. The method includes receiving an on-bottom pressure and anoff-bottom pressure. The method also includes determining a differentialpressure based upon the on-bottom pressure and the off-bottom pressure.The method also includes receiving a surface torque. The method alsoincludes determining a torque transmission coefficient based at leastpartially upon the differential pressure and the surface torque. Themethod also includes determining the total torque output at the drillbit based at least partially upon the differential pressure, the surfacetorque, and the torque transmission coefficient.

A computing system is also disclosed. The computing system includes atleast one processor and a storage medium connected to the at least oneprocessor. The storage medium includes instructions for configuring thecomputing system to perform operations. The operations include receivingan on-bottom pressure and an off-bottom pressure that are measured by apressure sensor. The, wherein the pressure sensor is at a surface abovea wellbore. The on-bottom pressure includes a pressure when a bottomhole assembly (BHA) is on a bottom of the wellbore. The off-bottompressure includes the pressure when the BHA is off of the bottom of thewellbore. The operations also include determining a differentialpressure that represents a difference between the on-bottom pressure andthe off-bottom pressure. The operations also include receiving a surfacetorque measured by a torque sensor. The surface torque is a torqueintroduced to a drill string by a top drive. The torque sensor iscoupled to the top drive. The drill string extends into the wellbore.The BHA is coupled to a lower end of the drill string. The BHA includesa mud motor and a drill bit. The operations also include determining atorque transmission coefficient based at least partially upon thedifferential pressure and the surface torque. The torque transmissioncoefficient is a positive unitless coefficient that is less than 1 andrepresents a torque between a rotor and stator rubber in the mud motor.The operations also include determining a total torque output at thedrill bit based at least partially upon the differential pressure, thesurface torque, and the torque transmission coefficient.

A non-transitory machine-readable storage medium is also disclosed. Thestorage medium has instructions stored thereon to configure a processorof a computing system to perform operations. The operations includereceiving an on-bottom pressure and an off-bottom pressure that aremeasured by a pressure sensor. The pressure sensor is at a surface abovea wellbore. The on-bottom pressure is a pressure when a bottom holeassembly (BHA) is on a bottom of the wellbore. The off-bottom pressureis the pressure when the BHA is off of the bottom of the wellbore. Theoperations also include determining a differential pressure thatrepresents a difference between the on-bottom pressure and theoff-bottom pressure. The operations also include receiving a surfacetorque measured by a torque sensor. The surface torque is a torqueintroduced to a drill string by a top drive. The torque sensor iscoupled to the top drive. The drill string extends into the wellbore.The BHA is coupled to a lower end of the drill string. The BHA includesa mud motor and a drill bit. The operations also include determining atorque transmission coefficient based at least partially upon thedifferential pressure and the surface torque. The torque transmissioncoefficient is a positive unitless coefficient that is less than 1 andrepresents a torque between a rotor and stator rubber in the mud motor.The operations also include determining a total torque output at thedrill bit based at least partially upon the differential pressure, thesurface torque, and the torque transmission coefficient. The totaltorque output is determined by a model. Determining the total torqueoutput includes multiplying a torque slope of the mud motor and thedifferential pressure to produce a first value, multiplying the surfacetorque and the torque transmission coefficient to produce a secondvalue, and adding the first value and the second value to produce thetotal torque output. The operations also include generating a signal inresponse to the total torque output. The signal causes one or moreparameters to vary. The one or more parameters include the on-bottompressure, the off-bottom pressure, an amount of the torque introducedinto the drill string by the top drive, a weight on the drill bit, arate of rotation of the drill string, the BHA, or both, a toolfacesetting of the BHA, a flow rate of a fluid being pumped into thewellbore, or a combination thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate embodiments of the presentteachings and together with the description, serve to explain theprinciples of the present teachings. In the figures:

FIG. 1 illustrates an example of a system that includes variousmanagement components to manage various aspects of a geologicenvironment, according to an embodiment.

FIG. 2 illustrates a schematic view of a wellsite, according to anembodiment.

FIG. 3A illustrates a perspective view of a mud motor showing externalcomponents thereof, according to an embodiment.

FIG. 3B illustrates a cross-sectional side view of the mud motor showinginternal components therein, according to an embodiment.

FIG. 3C illustrates a cross-sectional view of a power section of the mudmotor showing a rotor therein, according to an embodiment.

FIG. 3D illustrates a cross-sectional view of the power section showinga stator therein, according to an embodiment.

FIG. 4 illustrates a perspective view of the power section with aportion of the stator tube removed to show the rotor therein, accordingto an embodiment.

FIG. 5A illustrates motion of a single cavity of a 6/7 lobeconfiguration power section, and FIG. 5B illustrates a cross-sectionalview of a portion of FIG. 5A, according to an embodiment.

FIG. 6 illustrates a side view of a snapshot in time of differentcavities inside the power section, according to an embodiment.

FIG. 7 illustrates a graph showing a torque output curve for the powersection, according to an embodiment.

FIG. 8 illustrates a graph showing RPM output curves for the powersection, according to an embodiment.

FIG. 9 illustrates a graph showing the pressure along the length of thepower section during a performance test, according to an embodiment.

FIG. 10 illustrates a perspective view of the power section showingadditional force on the rotor at the top of the mud motor due to thepumping of the drilling fluid, according to an embodiment.

FIGS. 11A-11C illustrate graphs showing real-time drilling parametersduring well construction, according to an embodiment.

FIGS. 12A-12C illustrates graphs showing real-time drilling parametersduring stall conditions for the mud motor, according to an embodiment.

FIG. 13 illustrates a graph showing acoustic impedance for the mudmotor, according to an embodiment.

FIG. 14 illustrates a graph showing a comparison between the torqueoutput according to the power section specifications and the measuredsurface torque, according to an embodiment.

FIGS. 15A-15J illustrate graphs showing real-time mud motor automaticslide detection, according to an embodiment.

FIGS. 16A and 16B illustrate graphs showing real-time motor degradationindicators comparing the expected RPM output and measured RPM output,according to an embodiment.

FIG. 17 illustrates a flowchart of a method for deriving the downholetorque measurement below the mud motor, according to an embodiment.

FIG. 18 illustrates a flowchart of another method for deriving thedownhole torque measurement below the mud motor, according to anembodiment.

FIG. 19 illustrates a flowchart of another method for deriving thedownhole torque measurement below the mud motor, according to anembodiment.

FIG. 20 illustrates an example of a computing system for performing atleast a portion of one or more of the methods disclosed herein, inaccordance with some embodiments.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings and figures. In thefollowing detailed description, numerous specific details are set forthin order to provide a thorough understanding of the invention. However,it will be apparent to one of ordinary skill in the art that theinvention may be practiced without these specific details. In otherinstances, well-known methods, procedures, components, circuits, andnetworks have not been described in detail so as not to unnecessarilyobscure aspects of the embodiments.

It will also be understood that, although the terms first, second, etc.may be used herein to describe various elements, these elements shouldnot be limited by these terms. These terms are only used to distinguishone element from another. For example, a first object or step could betermed a second object or step, and, similarly, a second object or stepcould be termed a first object or step, without departing from the scopeof the present disclosure. The first object or step, and the secondobject or step, are both, objects or steps, respectively, but they arenot to be considered the same object or step.

The terminology used in the description herein is for the purpose ofdescribing particular embodiments and is not intended to be limiting. Asused in this description and the appended claims, the singular forms“a,” “an” and “the” are intended to include the plural forms as well,unless the context clearly indicates otherwise. It will also beunderstood that the term “and/or” as used herein refers to andencompasses any possible combinations of one or more of the associatedlisted items. It will be further understood that the terms “includes,”“including,” “comprises” and/or “comprising,” when used in thisspecification, specify the presence of stated features, integers, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, integers, steps,operations, elements, components, and/or groups thereof. Further, asused herein, the term “if” may be construed to mean “when” or “upon” or“in response to determining” or “in response to detecting,” depending onthe context.

Attention is now directed to processing procedures, methods, techniques,and workflows that are in accordance with some embodiments. Someoperations in the processing procedures, methods, techniques, andworkflows disclosed herein may be combined and/or the order of someoperations may be changed.

FIG. 1 illustrates an example of a system 100 that includes variousmanagement components 110 to manage various aspects of a geologicenvironment 150 (e.g., an environment that includes a sedimentary basin,a reservoir 151, one or more faults 153-1, one or more geobodies 153-2,etc.). For example, the management components 110 may allow for director indirect management of sensing, drilling, injecting, extracting,etc., with respect to the geologic environment 150. In turn, furtherinformation about the geologic environment 150 may become available asfeedback 160 (e.g., optionally as input to one or more of the managementcomponents 110).

In the example of FIG. 1 , the management components 110 include aseismic data component 112, an additional information component 114(e.g., well/logging data), a processing component 116, a simulationcomponent 120, an attribute component 130, an analysis/visualizationcomponent 142 and a workflow component 144. In operation, seismic dataand other information provided per the components 112 and 114 may beinput to the simulation component 120.

In an example embodiment, the simulation component 120 may rely onentities 122. Entities 122 may include earth entities or geologicalobjects such as wells, surfaces, bodies, reservoirs, etc. In the system100, the entities 122 can include virtual representations of actualphysical entities that are reconstructed for purposes of simulation. Theentities 122 may include entities based on data acquired via sensing,observation, etc. (e.g., the seismic data 112 and other information114). An entity may be characterized by one or more properties (e.g., ageometrical pillar grid entity of an earth model may be characterized bya porosity property). Such properties may represent one or moremeasurements (e.g., acquired data), calculations, etc.

In an example embodiment, the simulation component 120 may operate inconjunction with a software framework such as an object-based framework.In such a framework, entities may include entities based on pre-definedclasses to facilitate modeling and simulation. A commercially availableexample of an object-based framework is the MICROSOFT® .NET® framework(Redmond, Wash.), which provides a set of extensible object classes. Inthe .NET® framework, an object class encapsulates a module of reusablecode and associated data structures. Object classes can be used toinstantiate object instances for use in by a program, script, etc. Forexample, borehole classes may define objects for representing boreholesbased on well data.

In the example of FIG. 1 , the simulation component 120 may processinformation to conform to one or more attributes specified by theattribute component 130, which may include a library of attributes. Suchprocessing may occur prior to input to the simulation component 120(e.g., consider the processing component 116). As an example, thesimulation component 120 may perform operations on input informationbased on one or more attributes specified by the attribute component130. In an example embodiment, the simulation component 120 mayconstruct one or more models of the geologic environment 150, which maybe relied on to simulate behavior of the geologic environment 150 (e.g.,responsive to one or more acts, whether natural or artificial). In theexample of FIG. 1 , the analysis/visualization component 142 may allowfor interaction with a model or model-based results (e.g., simulationresults, etc.). As an example, output from the simulation component 120may be input to one or more other workflows, as indicated by a workflowcomponent 144.

As an example, the simulation component 120 may include one or morefeatures of a simulator such as the ECLIPSE™ reservoir simulator(Schlumberger Limited, Houston Tex.), the INTERSECT™ reservoir simulator(Schlumberger Limited, Houston Tex.), etc. As an example, a simulationcomponent, a simulator, etc. may include features to implement one ormore meshless techniques (e.g., to solve one or more equations, etc.).As an example, a reservoir or reservoirs may be simulated with respectto one or more enhanced recovery techniques (e.g., consider a thermalprocess such as SAGD, etc.).

In an example embodiment, the management components 110 may includefeatures of a commercially available framework such as the PETREL®seismic to simulation software framework (Schlumberger Limited, Houston,Tex.). The PETREL® framework provides components that allow foroptimization of exploration and development operations. The PETREL®framework includes seismic to simulation software components that canoutput information for use in increasing reservoir performance, forexample, by improving asset team productivity. Through use of such aframework, various professionals (e.g., geophysicists, geologists, andreservoir engineers) can develop collaborative workflows and integrateoperations to streamline processes. Such a framework may be consideredan application and may be considered a data-driven application (e.g.,where data is input for purposes of modeling, simulating, etc.).

In an example embodiment, various aspects of the management components110 may include add-ons or plug-ins that operate according tospecifications of a framework environment. For example, a commerciallyavailable framework environment marketed as the OCEAN® frameworkenvironment (Schlumberger Limited, Houston, Tex.) allows for integrationof add-ons (or plug-ins) into a PETREL® framework workflow. The OCEAN®framework environment leverages .NET® tools (Microsoft Corporation,Redmond, Wash.) and offers stable, user-friendly interfaces forefficient development. In an example embodiment, various components maybe implemented as add-ons (or plug-ins) that conform to and operateaccording to specifications of a framework environment (e.g., accordingto application programming interface (API) specifications, etc.).

FIG. 1 also shows an example of a framework 170 that includes a modelsimulation layer 180 along with a framework services layer 190, aframework core layer 195 and a modules layer 175. The framework 170 mayinclude the commercially available OCEAN® framework where the modelsimulation layer 180 is the commercially available PETREL® model-centricsoftware package that hosts OCEAN® framework applications. In an exampleembodiment, the PETREL® software may be considered a data-drivenapplication. The PETREL® software can include a framework for modelbuilding and visualization.

As an example, a framework may include features for implementing one ormore mesh generation techniques. For example, a framework may include aninput component for receipt of information from interpretation ofseismic data, one or more attributes based at least in part on seismicdata, log data, image data, etc. Such a framework may include a meshgeneration component that processes input information, optionally inconjunction with other information, to generate a mesh.

In the example of FIG. 1 , the model simulation layer 180 may providedomain objects 182, act as a data source 184, provide for rendering 186and provide for various user interfaces 188. Rendering 186 may provide agraphical environment in which applications can display their data whilethe user interfaces 188 may provide a common look and feel forapplication user interface components.

As an example, the domain objects 182 can include entity objects,property objects and optionally other objects. Entity objects may beused to geometrically represent wells, surfaces, bodies, reservoirs,etc., while property objects may be used to provide property values aswell as data versions and display parameters. For example, an entityobject may represent a well where a property object provides loginformation as well as version information and display information(e.g., to display the well as part of a model).

In the example of FIG. 1 , data may be stored in one or more datasources (or data stores, generally physical data storage devices), whichmay be at the same or different physical sites and accessible via one ormore networks. The model simulation layer 180 may be configured to modelprojects. As such, a particular project may be stored where storedproject information may include inputs, models, results, and cases.Thus, upon completion of a modeling session, a user may store a project.At a later time, the project can be accessed and restored using themodel simulation layer 180, which can recreate instances of the relevantdomain objects.

In the example of FIG. 1 , the geologic environment 150 may includelayers (e.g., stratification) that include a reservoir 151 and one ormore other features such as the fault 153-1, the geobody 153-2, etc. Asan example, the geologic environment 150 may be outfitted with any of avariety of sensors, detectors, actuators, etc. For example, equipment152 may include communication circuitry to receive and to transmitinformation with respect to one or more networks 155. Such informationmay include information associated with downhole equipment 154, whichmay be equipment to acquire information, to assist with resourcerecovery, etc. Other equipment 156 may be located remote from a wellsite and include sensing, detecting, emitting or other circuitry. Suchequipment may include storage and communication circuitry to store andto communicate data, instructions, etc. As an example, one or moresatellites may be provided for purposes of communications, dataacquisition, etc. For example, FIG. 1 shows a satellite in communicationwith the network 155 that may be configured for communications, notingthat the satellite may additionally or instead include circuitry forimagery (e.g., spatial, spectral, temporal, radiometric, etc.).

FIG. 1 also shows the geologic environment 150 as optionally includingequipment 157 and 158 associated with a well that includes asubstantially horizontal portion that may intersect with one or morefractures 159. For example, consider a well in a shale formation thatmay include natural fractures, artificial fractures (e.g., hydraulicfractures), or a combination of natural and artificial fractures. As anexample, a well may be drilled for a reservoir that is laterallyextensive. In such an example, lateral variations in properties,stresses, etc. may exist where an assessment of such variations mayassist with planning, operations, etc. to develop a laterally extensivereservoir (e.g., via fracturing, injecting, extracting, etc.). As anexample, the equipment 157 and/or 158 may include components, a system,systems, etc. for fracturing, seismic sensing, analysis of seismic data,assessment of one or more fractures, etc.

As mentioned, the system 100 may be used to perform one or moreworkflows. A workflow may be a process that includes a number ofworksteps. A workstep may operate on data, for example, to create newdata, to update existing data, etc. As an example, a may operate on oneor more inputs and create one or more results, for example, based on oneor more algorithms. As an example, a system may include a workfloweditor for creation, editing, executing, etc. of a workflow. In such anexample, the workflow editor may provide for selection of one or morepre-defined worksteps, one or more customized worksteps, etc. As anexample, a workflow may be a workflow implementable in the PETREL®software, for example, that operates on seismic data, seismicattribute(s), etc. As an example, a workflow may be a processimplementable in the OCEAN® framework. As an example, a workflow mayinclude one or more worksteps that access a module such as a plug-in(e.g., external executable code, etc.).

System and Method for Determining a Transfer of Torque from the Surfaceto a Drill Bit when Drilling with a Mud Motor

FIG. 2 illustrates a schematic view of a wellsite 200, according to anembodiment. The wellsite 200 may include a drilling rig 210 positionedat the surface 220. The drilling rig 210 may be positioned over awellbore 230 that extends into a subterranean formation 240. A drillstring 250 may extend from the drilling rig 210 into the wellbore 230.The drilling rig 210 may include surface torque equipment (e.g., a topdrive) 212 that may be configured to cause the drill string 250 torotate. This generates surface rotations per minute (RPM) and surfacetorque. A bottom hole assembly (BHA) 260 may be coupled to a lower endof the drill string 250. As described in greater detail below, the BHA260 may include a motor (e.g., a mud motor) and a drill bit. There maybe a torque below the motor, which may be the same as or different fromthe surface torque (e.g., when the BHA 260 is on-bottom in the wellbore230).

FIG. 3A illustrates a perspective view of a mud motor 300 showingexternal components thereof, and FIG. 3B illustrates a cross-sectionalside view of the mud motor 300 showing internal components therein,according to an embodiment. As shown in FIG. 3A, the external componentsmay include a top sub 310, a power section 320, a surface adjustablebent housing 330, a near-bit stabilizer 340, a drive shaft 350, or acombination thereof. The near-bit stabilizer 340 and/or the drive shaft350 may be coupled to a drill bit 360. As shown in FIG. 3B, the internalcomponents may include the power section 320, a transmission section370, a bearing section 380, and the drive shaft 350. The power section320 transforms hydraulic power into mechanical power.

FIG. 3C illustrates a cross-sectional view of the power section 320showing a rotor 322 therein, and FIG. 3D illustrates a cross-sectionalview of the power section 320 showing a stator 324 therein, according toan embodiment. The power section 320 may include the rotor (e.g., movingpart) 322 and the stator (e.g., stationary part) 324. The rotor 322 maybe made of steel. The stator 324 may be or include a metal tube withrubber 326 bonded inside. The stator tube 324 may have a circularcross-section with the rubber 326 taking the form of one or more lobes.A thin wall stator 324 has the metal tube in the form of the lobeproviding extra stiffness to add additional sealing capability to thestator 324.

FIG. 4 illustrates a perspective view of the power section 320 with aportion of the stator tube 324 removed to show the rotor 322 therein,according to an embodiment. A portion of the fluid may be trappedbetween the rotor 322 and the rubber lining 326. The space filled bythis trapped fluid between the rotor 322 and rubber lining 326 is calleda cavity 328, and the boundaries between these cavities 328 are calledsealing lines and sealing surfaces.

FIG. 5A illustrates motion of a single cavity of a 6/7 lobeconfiguration power section 320, and FIG. 5B illustrates across-sectional view of a portion of FIG. 5A, according to anembodiment. Each cavity 328 may move from up to down with both axialprogression and orbital movement in a spiral-like motion when the fluidis travelling from up to down the power section 320. During this motion,the pressure inside the cavity 328 may change as the cavity 328 ismoving along the power section 320. FIG. 6 illustrates a side view of asnapshot in time of different cavities 328 inside the power section 320,according to an embodiment.

If the sealing lines and sealing surfaces are working, there may be noexchange of fluid between cavities 328 as the cavities 328 may beisolated from each other. However, sometimes there may be leakagebetween these cavities 328. The pressure may decrease almost linearlybetween the first cavities 328 that are open to the inlet of the powersection 320 and the last cavities 328 that open to the outlet of thecavities 328. The pressure difference between two adjacent cavities 328in the axial position (ΔP) yields the following equation:

$\begin{matrix}{{\Delta P} = \frac{{{Inlet}{Pressure}} - {{Outlet}{Pressure}}}{{Number}{of}{closed}{cavities}}} & (1)\end{matrix}$

There are two types of sealing lines: (1) low pressure sealing lines:separating cavities 328 with pressure difference equal to 1 ΔP; and (2)high pressure sealing lines: separating cavities 328 with a pressuredifference equal to n_(S) ΔP, where n_(S) is the number of lobes on thestator 324. These sealing lines may define the pressure separationbetween the cavities 328. There is a (e.g., direct) link between theoutput torque that the motor 300 is providing to the drill bit 360 andthe pressure differential capability of the mud motor 300. Moreparticularly, the torque output by the motor power section 320 followsthe curve shown in the graph in FIG. 7 , which represents a torqueoutput curve for the power section 320, according to an embodiment.

The other component of the mechanical power output by the motor 300 isthe rotational speed RPM_(m). This RPM_(m) also depends on the overallactive differential pressure across the motor power section ΔP_(a). FIG.8 illustrates a graph showing RPM output curves for the power section320, according to an embodiment. This RPM_(m) may follow one or more ofthe curves.

FIG. 9 illustrates a graph showing the pressure along the length of thepower section 320 during a performance test, according to an embodiment.Executing a performance test of a motor power section 320 (e.g., using adynamometer to monitor the pressure profile along the length of powersection) may yield the curves shown in FIG. 9 . The performance test mayinclude gradually increasing the torque output of the motor 300 withtime until the motor 300 stalls. One area of the motor 300, which maytake up the pressure, is the inlet portion as the torque and thedifferential pressure increases, whereas the output side of the motor300 is almost constant during the test, regardless of the increase intorque.

Mud Motor Effects on Surface Measurements

Surface measurements during well construction may include the blockposition to estimate the rate of penetration (ROP), the hookload toobtain the weight on bit (WOB), the surface rotation per minute (RPM) toderive the bit RPM, the standpipe pressure (SPP) to help assess thepressure balance, the flow rate that provides the pumping regime, and/orthe surface torque to attempt to obtain the current torque output at thebit and comprehend the efficiency of the well construction. Thesemeasurements may be used to monitor, advise, and/or autonomously controlthe well construction. The interpretation of one or more (e.g., four) ofthese measurements may be (e.g., directly) affected by the presence of(or lack of) the mud motor 300 inside the BHA 260, whether it be in thesteering mode or in power mode when combined with a rotary steerablesystem (RSS).

Block Position and ROP

In terms of the block position and ROP, the addition of the mud motor300 inside of the BHA 260 may produce extra power at the drill bit 360,which in most cases may result in a higher ROP compared with the sameBHA without the mud motor 300. This condition is particularly true whenoperating the mud motor 300 in a power situation.

Hookload, Surface WOB (WOB_(S)) and Downhole WOB (WOB_(D))

The hookload may be used to derive the downhole WOB applied to the drillbit 360. The presence of or lack of the mud motor 300 may alter theinterpretation. When the mud motor 300 is present, there is additionalweight with the fluid pushing the top portion of the rotor 322 which isopen as shown in FIG. 10 . This extra force contributes marginally tothe downhole WOB. When the mud motor 300 is close to stalling, thisforce may cause a positive feedback loop that may accelerate thestalling process. In essence, when stalling, the mud motor torque may behigh. This high torque may result in increased pressure on the inletportion of the mud motor 300. This inlet pressure increase may increaseF_(Fluid) described in FIG. 10 , which may lead to increased WOB, andthe increased WOB may increase the torque, and so on.

Surface RPM and Downhole RPM

Using the surface RPM (RPM_(S)) to determine the overall RPM of thedrill bit 360 may be calculated using following equation:

RPM _(Bit) =RPM _(M) +RPM _(S)  (2)

Equation (2) means that when there is a mud motor 300 in the BHA 260,the bit RPM may be the sum of the surface RPM and the motor RPM shownpreviously in FIG. 7 .

Standpipe Pressure (SPP)

The standpipe pressure is a measurement to identify and/or preventpressure imbalance inside the wellbore 230 currently being drilled. Assuch, the standpipe pressure is a decisive measurement that is monitoredclosely to avoid effects of a kick and/or blowout. The mud motor effecton this measurement may be seen in FIG. 9 . There is often a differencein pressure above the mud motor 300 when the drill bit 360 is on-bottomvs. when it is off-bottom. FIGS. 11A-11C illustrate drilling parameters(e.g., surface WOB, ROP, surface torque, standpipe pressure, etc.) whenoperating the mud motor 300 with the standpipe pressure increasing withincreased WOB and resulting drill bit torque demand. This added pressureabove the mud motor 300 may directly translate to the standpipepressure. The difference in pressure while raising the WOB may be morethan 2,000 psi in some cases.

The standpipe pressure may be used to infer imbalance wellbore pressure.The presence of the mud motor 300 may change the pressure regime becauseadditional torque at the bit 360 is used to construct the wellbore 230.

Flow Rate

Under normal steady-state drilling conditions, even if the mud motor 300is present in the BHA 260, the flow rate in the entire drill string 250and BHA 260 is more or less the same as the surface flow rate measureddirectly at the pumps' output. When operating with an RSS tool, theturbine RPM, which is inside the RSS tool, can be used to derive theactual downhole flow rate. This information may be useful because itallows the comparison of the surface flow rate from the pumps and thedownhole flow rate at the BHA 260. With steady-state drillingconditions, both the surface flow rate and the downhole flow rate may beequal.

When the mud motor 300 is stalling, the operation becomes verydifferent. As shown in FIGS. 12A-12C, when the WOB is increased to thestall point, the mud motor stall may be detected at the surface by thesudden jump in standpipe pressure. During this time, although thesurface flow rate remains very steady, the downhole flow rate below themud motor 300 experiences a sudden decrease related to the acousticimpedance of the mud motor 300. When increase in pressure happens at atime frame slower than the two-way travel time of the drilling fluid, itmay result in a sharp decrease of flow rate below the mud motor 300. Thedecrease of flow rate may be determined with the equation:

$\begin{matrix}{{{\Delta Q} = {- \frac{\Delta P_{a}}{Z}}},} & (3)\end{matrix}$

where Z=the acoustic impedance of the assembly, ΔQ=the diminution offlow rate, and ΔP_(a)=the sudden increase of pressure.

This condition may affect the drilling. FIG. 13 illustrates a scenariowhere drilling is taking place with a steady surface flow rate of 600gal/min (gpm). A stringer is encountered downhole, and the pressureimmediately increases by 1,200 psi. Assuming an impedance of 3 psi/gpm,it would result in a decrease of flow of about 400 gpm. In terms of howthe mud motor 300 operates, this implies that instead of stalling alongthe 600 gpm curve, the stall may take place along the 200 gpm curve,meaning that the stall would take place much faster than anticipated.

Surface Torque and Downhole Torque

Referring again to FIG. 7 , it may be seen that below a certain pressuredifferential ΔP_(limit), the torque output from the mud motor 300 islinear with respect to the differential pressure. This is because thetorque generated by the rotor 322 comes almost exclusively from theimbalance in pressure between the cavities 328. The torque slope for thelinear regime part may be defined as the dependency between the torqueand the differential pressure:

$\begin{matrix}{{Torque}_{slope} = \frac{T}{\Delta P_{a}}} & (4)\end{matrix}$

This torque slope may be geometry-driven and (e.g., directly) linked tothe kinematics of the power section 320. It may not (or may partially)depend on the flow rate, the rubber type, the type of fluid, theinterference fit, the power section length, or a combination thereof.When operating the power section 320 under normal regime, a user may useEquation 2 to model the torque output.

FIG. 14 illustrates a graph showing a comparison between the torqueoutput according to the power section specifications and the measuredsurface torque, according to an embodiment. The surface torque refers tothe torque introduced to the drill string 230 at the surface (e.g., bythe top drive 212). The surface torque does not reflect the behavior ofthe mud motor 300 downhole. The reason is that, when the power section320 is operating, the top part of the rotor 322 may be free. As thelower part of the rotor 322 is (e.g., directly) connected torsionally tothe drill bit 360, this means that when the mud motor 300 is present,the torque generated at the bit 360 is from the rotor 322. Thecontribution of the surface top drive torque is coming from the contactpressure between the stator elastomer 326 and the rotor 322. Thiscontribution may be less than (e.g., minimal compared to) the outputtorque coming from the pressure differential between cavities 322. Thismeans that there is a torque discontinuity between the upper part of thebottom hole assembly (BHA) 260 (e.g., above the motor 300) and the lowerpart of the BHA 260 (e.g., below the motor 300). In one example, ifthere is perfect lubrication between the stator rubber 326 and the rotor322, the contribution from the surface top drive 212 to the torqueoutput may be nearly zero.

The total torque output (T_(Total)) in the lower part of the motor 300,in terms of the torque that is coming from the surface top drive(T_(S),) and the torque being generated by the rotor (T_(M)), is shownin Equation 3:

T _(Total) =T _(M) +αT _(S)  (5)

In this equation, the variable α is a positive unitless coefficient thatis less than 1 and represents the transmission of torque between thestator rubber 326 and the rotor 322 via frictional contact pressure. Thevalue of a may depend on a number of factors such as:

-   -   The rubber type and rubber manufacturing process: the bigger the        frictional capability of the rubber, the bigger α may be.    -   The interference fit which is how tight the rotor 322 is fitting        inside the stator 324: the tighter the interference fit, the        bigger α may be.    -   The rotor type and polishing process: the smaller frictional        capability of the rotor 322, the smaller α may be.    -   The lobe configuration: a higher lobe count results in a higher        α value.    -   The profile of the power section 322: frictional contact is        playing a role here.    -   The drilling fluid and its sand and solid content: this is the        lubrication capability of the drilling fluid.    -   The downhole temperature: due to the rubber thermal expansion,        the higher the temperature, the higher the value of α.    -   The downhole pressure: This depends on the difference between        the internal pressure and the external pressure and also on the        lobe deformation of the rubber 326.    -   The compatibility between the mud and the rubber 326: the more        the swelling of the rubber 326 due to the mud, the higher α may        be.    -   The surface RPM and the rotor RPM: This depends on both the        relative RPM between the surface RPM and the rotor RPM and also        the absolute value of both RPMs.    -   The flow rate: this effect is still uncharacterized.

The derivation of this positive unitless coefficient α reflects thetransmission of torque between the stator rubber 326 and the rotor 322via frictional contact pressure.

Digital Well Construction Workflows

With greater understanding of how to interpret the surface measurementswhen a mud motor is present inside the BHA 260, examples are presentedbelow showing how to use this information for monitoring, advising,and/or controlling the drilling process when constructing the wellbore230 with the mud motor 300. This understanding of the motor physics canbe used both in the planning phase (e.g., while preparing for a drillingoperation) and/or in the execution phase. The path towards an autonomouswell construction may be explored through analyzing the mechanicalspecific energy (MSE), an automatic slide detection for steering withthe mud motor 300, an abnormal pressure detection, and a real-time mudmotor efficiency and degradation.

MSE Calculation

The MSE may be used to monitor the drilling efficiency. Nonetheless,when the mud motor 300 is present inside the BHA 260, its estimation ofthe energy consumed at the drill bit 360 often suffers from a lack ofunderstanding of the mud motor physics. When there is no mud motor, aformula for calculating MSE is:

$\begin{matrix}{{MSE} = {{{MSE}_{Axial} + {MSE}_{Tor}} = {\frac{{WOB}_{S}}{A_{bit}} + \frac{120\pi{RPM}_{S}T_{S}}{A_{bit}{ROP}}}}} & (6)\end{matrix}$

where A_(bit) is the bit area, WOB_(S), RPM_(S), and T_(S) are thesurface weight-on-bit, the surface RPM, and the surface torque,respectively. This equation may be useful as long as the focus is on thesurface energy input when there is no motor 300 inside of the BHA 260.

However, most BHAs 260 include a mud motor 300 either on steering modeor on power mode to gain extra efficiency while constructing thewellbore 230. The formula may evolve when the motor 300 is being used.In addition, the MSE may be used to determine how efficiently the drillbit 360 is cutting the rock and making the wellbore 230 from theinitially given energy. The new MSE formula will look like:

$\begin{matrix}{{{MSE} = {{{MSE}_{Axial} + {MSE}_{Tor}} = {\frac{{WOB}_{D}}{A_{bit}} + \frac{120\pi{RPM}_{Bit}T_{Total}}{A_{bit}{ROP}}}}}{{MSE} = {\frac{{WOB}_{D}}{A_{bit}} + \frac{120{\pi\left( {{RPM}_{S} + {RPM}_{M}} \right)}\left( {T_{M} + {\alpha T_{S}}} \right)}{A_{bit}{ROP}}}}} & (7)\end{matrix}$

where WOB_(D) is downhole weight-on-bit, and a is the positive unitlesstorque transmission coefficient. This formula may be used to evaluatethe efficiency of the drill bit 360. In many scenarios, the MSE may beused relatively by observing the trends in particular formations 240 andthen a decrease or increase in the trends may be used to detectparticular formations 240 or efficiency issues. However, when the mudmotor 300 is present, not taking account of the motor kinematics couldlead to wrong conclusions being made.

Automatic Slide Detection

Using downhole mud motors 300, directional drillers may be able to kickoff the wellbore 230, build angle, and drill tangent sections. Thesurface adjustable bend housing may be used to steer the bit 360 to adesired direction. After orienting the bend to a specific direction(i.e., tool face angle), and by not allowing drill string rotation whiledrilling, a slide mode drilling operation may be triggered. A precisetool face orientation during the slide drilling may be used to achievedesired targets. However, many downhole drilling conditions may affectthe slide performance such as the reactive torque, stalling of the mudmotor 300, drilling through different formations, difficultiestransferring weight to the bit 360, etc.

Directional drillers aim to maintain a predetermined ROP, toolface (TF),and transfer weight to the drill bit (WOB) without stalling the mudmotor 300 to maintain high drilling efficiency. On the other hand, byincreasing the hole depth, drillstring friction and drag may increase.Hence, transferring WOB and controlling TF performance may be moredifficult as the depth increases. As a result, maintaining sufficientROP and providing the desired trajectory to the target may be moreproblematic. Often, to increase the efficiency of the transfer ofweight, drillers may rock the pipe while sliding using different typesof systems.

Using mud motor behavior and its kinematics with surface measured data(i.e., surface torque), a user can automatically perform the piperocking similar to the method described above. This may increase theability to maintain sufficient ROP and still deliver a desired toolfaceorientation. In addition, this understanding of the mud motor behaviorallows the conception of an automated slide detection which is criticalto any steering advisor workflow.

The method may be used to detect in real-time the slides performed bythe mud motor 300 based (e.g., solely) on analyzing the surface data.This method is developed based on understanding the mud motor physicalbehavior in addition to the changes in torque, RPM, WOB, ROP,differential pressure, etc. FIGS. 15A-15J illustrate graphs showingreal-time mud motor automatic slide detection, according to anembodiment.

Abnormal Pressure Detection

Abnormal standpipe pressure is one of the indicators of a disfunction inthe drilling fluid hydraulic system. This condition is defined as anobservation of any change in standpipe pressure due to undesired eventsoccurring during the well construction process. A greater perception ofthe mud motor physics allows for deriving an automated abnormal pressuredetection based on a probabilistic approach. The model may havedifferent physics-based priors depending on whether the mud motor 300 ispresent or not. In the case when the mud motor 300 is present, the modelmay separate the slide drilling from the rotary drilling and use themotor pressure knowledge to obtain a prior approximation. Thephysics-based prior will look like:

$\left\{ \begin{matrix}{{{no}{motor}:{SPP}} = {\beta_{Q}Q^{1.8}}} \\{{motor},{{{slide}{drilling}:{SPP}} = {{\beta_{Q}Q^{1.8}} + {\beta_{W}{WOB}}}}} \\{{motor},{{{rotary}{drilling}:{SPP}} = {{\beta_{Q}Q^{1.8}} + {\beta_{T}T_{S}}}}}\end{matrix} \right.$

Real-Time Mud Motor Efficiency and Degradation

In spite of mud motors 300 being one of the most commonly used toolsinside the BHA 260 as mentioned previously, there is still a lack ofreliable procedures for monitoring and maintaining the well-being of themud motors 300 during well construction. This problem results inmaintenance and fleet management costs as well as unpredictable andcostly failures. In addition, there may be, in some cases, efficiencylosses due to the degradation of the mud motor 300 over time. The methodpresented here aims to estimate, in real time, the energy output and theefficiency of the mud motor 300 based on analyzing both surface anddownhole data combined with the knowledge of the mud motor physics.

The method may rely on defining a motor wear indicator by comparing theexpected RPM based on the motor power section specifications and thedownhole output RPM measured with downhole tools below the motor 300.FIGS. 16A and 16B illustrate an example of the real time motorefficiency analysis from a drilling operation with a degradation rate ofabout 3.7%/100 ft. FIG. 16A shows a near-constant flow rate and a slightvariation in standpipe pressure. Yet, the RPM reduction can be seenclearly in FIG. 16B suggesting that this RPM reduction is indeed theresult of a mud motor degradation. This degradation rate may be used toassess the expected ROP reduction and also the expected durability ofthe mud motor 300 to avoid costly failures.

Workflows for Determining α

The workflows for determining a may be divided into two categories: (1)real-time execution workflows, and (2) planning workflows.

Real-Time Execution Workflows:

The real-time execution workflows for deriving and using a forunderstanding the torque transmission from surface to the lower part ofthe BHA below the motor 300 may be based at least partially on updatingthe value of a with available measurement of torque downhole and/orusing a model of a variations with respect to drilling parametersincluding temperature and pressure and mud motor conditions.

FIG. 17 illustrates a flowchart of a method for deriving the downholetorque measurement below the mud motor 300, according to an embodiment.More particularly, FIG. 17 may be used to determine (e.g., estimate) thetorque transmission coefficient α during execution using downhole torquemeasurements.

FIG. 18 illustrates a flowchart of another method for deriving thedownhole torque measurement below the mud motor 300, according to anembodiment. The method in FIG. 18 may be based at least partially uponartificial intelligence (AI) and/or machine learning (ML) in real-time.The model may be trained on available offset data prior to the wellconstruction execution.

Planning Workflows

For the planning, a similar AI/ML method may be used. In addition, oneor more finite element analysis (FEA) models and/or analytical modelsmay also or instead be used.

How to Use the Derived Value of α

In one embodiment, the a values may be used during execution for:

-   -   displaying the value of the torque transmission coefficient to        better select the operating parameters by the user.    -   to automatically determine or detect a mud motor degradation        coefficient.    -   to automatically determine or detect a sliding mode from a        rotating mode.    -   to automatically determine or derive alarms for abnormal        pressure detection.    -   to select appropriate:        -   mud motors        -   interference fit between the rotor and the stator        -   rotors and their type of polishing        -   rubbers for the stator        -   drilling fluids        -   BHAs        -   derive optimized planned trajectory        -   derive appropriate drilling parameters ranges

Thus, the present disclosure provides a method of calculating the torquetransmission coefficient α from the top drive to below the motor 300using downhole torque measurement below the motor 300. The method mayalso be used to derive, in real-time, the value of the torquetransmission coefficient α via a ML/AI model ƒ using the function α=ƒ(Temp, Pressure, RPM, WOB, ΔP_(a), flow). The method may also be used toderive, in real-time, the value of the torque transmission coefficient αvia physical model based on analytical model g using the function α=g(Temp, Pressure, RPM, WOB, ΔP_(a), flow). The method may also be used toderive, in real-time, the value of the torque transmission coefficient αvia Finite element model FE using the function α=FE (Temp, Pressure,RPM, WOB, ΔP_(a), flow). The method may also be used to display thevariation of torque transmission coefficient α in either a log view or adirect parameter view. The method may also be used to determine the mudmotor degradation coefficient using the derived value of the torquetransmission coefficient α. The method may also be used to detect (e.g.,automatically) the sliding mode and the rotating mode while performingdirectional drilling with the mud motor 300 using the derived value ofthe torque transmission coefficient α. The method may also be used toderive alarms regarding abnormal pressure detection using the derivedvalue of the torque transmission coefficient α. The method may also beused to derive the torque transmission coefficient α by analyzing offsetdata fed inside a ML/AI model. The method may also be used to derive thetorque transmission coefficient α by analyzing offset data fed inside ananalytical model depending on the drilling parameters and the drillingconditions. The method may also be used to derive the torquetransmission coefficient α by analyzing offset data fed inside a finiteelement analysis (FEA) model depending on the drilling parameters andthe drilling conditions. The method may also be used to select one ormore of the following using the computed value of torque transmissioncoefficient α:

-   -   type of mud motor power section;    -   value of the power section interference fit to be used;    -   type of rubber to be used;    -   type of rotor and the polishing scheme;    -   type of drilling fluids; and/or    -   the range of drilling parameters to be used including RPM, WOB,        differential pressure, flow rate.

The method may also be used to derive a planned trajectory of a wellboreusing the computed torque transmission coefficient α. The method mayalso be used to derive a BHA to drill the wellbore using the computedtorque transmission coefficient α. The method may also be used to deriveone or more pipe rocking parameters based on the computed torquetransmission coefficient α.

FIG. 19 illustrates a flowchart of another method 1900 for deriving thedownhole torque measurement below the mud motor 300 (e.g., at the drillbit 360), according to an embodiment. An illustrative order of themethod 1900 is provided below; however, one or more portions of themethod 1900 may be performed in a different order, performedsimultaneously, combined, repeated, or omitted.

The method 1900 may include receiving an on-bottom pressure, as at 1905.The method 1900 may also include receiving an off-bottom pressure, as at1910. The on-bottom pressure may include a pressure when the BHA 260 ison the bottom of the wellbore 230 (e.g., during drilling). Theoff-bottom pressure may include the pressure when the BHA 260 is off ofthe bottom of the wellbore 230 (e.g., when not drilling). The on-bottompressure and/or the off-bottom pressure may be measured by a pressuresensor. The pressure sensor may be at the surface 220 above the wellbore230 (e.g., on the drilling rig 210).

The method 1900 may also include determining a differential pressure, asat 1915. The differential pressure may be based upon the on-bottompressure and the off-bottom pressure. The differential pressure may be adifference between the on-bottom pressure and the off-bottom pressure.

The method 1900 may also include receiving a surface torque, as at 1920.The surface torque may include a torque introduced to the drill string250 by the top drive 212 (or other rotation device). The surface torquemay be measured by a torque sensor. The torque sensor may be on thedrilling rig 210 (e.g., coupled to the top drive 212).

The method 1900 may also include determining a torque transmissioncoefficient, as at 1925. The torque transmission coefficient may bebased at least partially upon the differential pressure measurement andthe surface torque measurement. The torque transmission coefficient maybe a positive unitless coefficient that is less than 1 and representsthe torque between the rotor 322 and the stator rubber 326 in the mudmotor 300.

In one embodiment, determining the torque transmission coefficient mayinclude multiplying a torque slope of the mud motor 330 and thedifferential pressure measurement to produce a first value. Determiningthe torque transmission coefficient may also include subtracting thefirst value from a torque below the mud motor 230 to produce a secondvalue. Determining the torque transmission coefficient may also includedividing the second value by the surface torque to produce the torquetransmission coefficient.

The torque transmission coefficient may also be determined based atleast partially upon a temperature in the wellbore 230 (e.g., measuredby the BHA 260), a pressure in the wellbore 230 (e.g., measured by theBHA 260), a rate of rotation of the drill string 250 and/or BHA 260 inthe wellbore 230, a weight on the drill bit 360 in the wellbore 230, thedifferential pressure measurement, a flow rate of a fluid into thewellbore 230, or a combination thereof. The torque transmissioncoefficient may be determined using a machine learning (ML) artificialintelligence (AI) model, a physical model, a finite element (FE) model,or a combination thereof.

The method 1900 may also include determining a total torque output, asat 1930. The total torque output may be determined at the BHA 260 (e.g.,at the drill bit 360). The total torque output may be determined basedat least partially upon the differential pressure measurement, thesurface torque measurement, the torque transmission coefficient, or acombination thereof. The total torque output may be determined by amodel.

Determining the total torque output may include multiplying a torqueslope of the mud motor 330 and the differential pressure measurement toproduce a first value. Determining the total torque output may alsoinclude multiplying the surface torque measurement and the torquetransmission coefficient to produce a second value. Determining thetotal torque output may also include adding the first value and thesecond value to produce the total torque output.

The method 1900 may also include determining that a performance of themud motor is degrading, as at 1940. The determination may be in responseto the total torque output deviating from an expected torque output bymore than a predetermined torque threshold.

The method 1900 may also include determining that the drill string 250is sliding in the wellbore 230, as at 1945. The determination may be inresponse to the total torque output being less than a predeterminedtorque threshold. The method 1900 may also or instead includedetermining that the drill string 250 is rotating in the wellbore 230,as at 1950. The determination may be in response to the total torqueoutput being greater than the predetermined torque threshold.

The method 1900 may also include determining that the BHA 260 hasencountered an abnormal pressure event in the subterranean formation240, as at 1955. The determination may be in response to the torquetransmission coefficient, the total torque output, or both. The abnormalpressure event may be or include a region of the subterranean formation240 that has a pressure that is greater than a predetermined upperpressure threshold or less than a predetermined lower pressurethreshold. The abnormal pressure event may alter the behavior of the BHA260 (e.g., the mud motor 300). As described below, the abnormal pressureevent may be an indication of an influx, a blockage, a bit-ballingevent, the mud motor 300 stalling, downhole losses, or a combinationthereof.

Determining that the BHA 260 has encountered an abnormal pressure eventmay include measuring a first standpipe pressure (SPP) at the surface220. Determining that the BHA 260 has encountered an abnormal pressureevent may also include determining a second SPP at the surface 220.Determining that the BHA 260 has encountered an abnormal pressure eventmay also include determining that first SPP differs from the second SPPby more than a predetermined pressure.

Determining the second SPP may include multiplying a first constant anda flow rate squared to produce a first value. The flow rate is of afluid being pumped into the wellbore 230. Determining the second SPP mayalso include multiplying a second constant, the flow rate squared, and adepth of the drill bit 360 to produce a second value. Determining thesecond SPP may include multiplying a third constant and the total torqueoutput to produce a third value. Determining the second SPP may includemultiplying a fourth constant and a weight on the drill bit 360 toproduce a fourth value. Determining the second SPP may include addingthe first value, the second value, the third value, the fourth value,and a fifth constant to produce the second SPP. The first, second,third, fourth, and fifth constants are different.

The method 1900 may also include determining a torque transmissionissue, as at 1960. The torque transmission issue may be an issue orproblem that prevents the at least a portion of the torque from beingtransmitted from the surface (e.g., the top drive 212) to the drill bit360. The torque transmission issue may be determined based at leastpartially upon the abnormal pressure event, a mechanical specific energy(MSE), or both.

The method 1900 may also include generating a display, as at 1965. Thedisplay may show the torque transmission coefficient, the total torqueoutput, the performance of the mud motor 300, the location(s) where thedrill string 250 is slipping and/or rotating in the wellbore 230, thelocation(s) of abnormal pressure events in the wellbore 230, thelocation(s) of torque transmission issues, or a combination thereof.

The method 1900 may also include determining or performing a (e.g.,wellsite) action, as at 1970. The wellsite action may be determined orperformed based at least partially upon the torque transmissioncoefficient, the total torque output, the performance of the mud motor300, the slipping and/or rotating of the drill string 250, the abnormalpressure events, the torque transmission issues, or a combinationthereof. In one embodiment, performing the wellsite action may includegenerating and/or transmitting a signal (e.g., using the computingsystem 1400) which instructs or causes a physical action to take place.In another embodiment, performing the wellsite action may includephysically performing the action (e.g., either manually orautomatically).

Illustrative physical actions may include, but are not limited to,varying the off-bottom pressure, varying the on-bottom pressure, varyingthe weight on the drill bit 360, varying a rate of rotation of the drillstring 250 at the surface 220 (e.g., using the top drive 212), varyingan amount of torque introduced into the drill string 250 at the surface220 (e.g., using the top drive 212), varying a toolface setting of theBHA 260 (e.g., while sliding), varying the flow rate of the fluid beingpumped into the wellbore 230, checking for pack-off, checking forplugged nozzles in the drill bit 360, checking for blockages in thedrill string 250 and/or BHA 260, determining location(s) of washouts inthe wellbore 230, varying the drilling mud, circulating one or morepills to vary the pressure in the wellbore 230, stopping drilling,changing the BHA 260, checking the pumps for leaks or damage, or acombination thereof.

In some embodiments, the methods of the present disclosure may beexecuted by a computing system. FIG. 20 illustrates an example of such acomputing system 2000, in accordance with some embodiments. Thecomputing system 2000 may include a computer or computer system 2001A,which may be an individual computer system 2001A or an arrangement ofdistributed computer systems. The computer system 2001A includes one ormore analysis modules 2002 that are configured to perform various tasksaccording to some embodiments, such as one or more methods disclosedherein. To perform these various tasks, the analysis module 2002executes independently, or in coordination with, one or more processors2004, which is (or are) connected to one or more storage media 2006. Theprocessor(s) 2004 is (or are) also connected to a network interface 2007to allow the computer system 2001A to communicate over a data network2009 with one or more additional computer systems and/or computingsystems, such as 2001B, 2001C, and/or 2001D (note that computer systems2001B, 2001C and/or 2001D may or may not share the same architecture ascomputer system 2001A, and may be located in different physicallocations, e.g., computer systems 2001A and 2001B may be located in aprocessing facility, while in communication with one or more computersystems such as 2001C and/or 2001D that are located in one or more datacenters, and/or located in varying countries on different continents).

A processor may include a microprocessor, microcontroller, processormodule or subsystem, programmable integrated circuit, programmable gatearray, or another control or computing device.

The storage media 2006 may be implemented as one or morecomputer-readable or machine-readable storage media. Note that, while inthe example embodiment of FIG. 20 storage media 2006 is depicted aswithin computer system 2001A, in some embodiments, storage media 2006may be distributed within and/or across multiple internal and/orexternal enclosures of computing system 2001A and/or additionalcomputing systems. Storage media 2006 may include one or more differentforms of memory including semiconductor memory devices such as dynamicor static random access memories (DRAMs or SRAMs), erasable andprogrammable read-only memories (EPROMs), electrically erasable andprogrammable read-only memories (EEPROMs) and flash memories, magneticdisks such as fixed, floppy and removable disks, other magnetic mediaincluding tape, optical media such as compact disks (CDs) or digitalvideo disks (DVDs), BLURAY® disks, or other types of optical storage, orother types of storage devices. Note that the instructions discussedabove may be provided on one computer-readable or machine-readablestorage medium, or may be provided on multiple computer-readable ormachine-readable storage media distributed in a large system havingpossibly plural nodes. Such computer-readable or machine-readablestorage medium or media is (are) considered to be part of an article (orarticle of manufacture). An article or article of manufacture may referto any manufactured single component or multiple components. The storagemedium or media may be located either in the machine running themachine-readable instructions, or located at a remote site from whichmachine-readable instructions may be downloaded over a network forexecution.

In some embodiments, computing system 2000 contains one or more torquemodule(s) 2008. It should be appreciated that computing system 2000 ismerely one example of a computing system, and that computing system 2000may have more or fewer components than shown, may combine additionalcomponents not depicted in the example embodiment of FIG. 20 , and/orcomputing system 2000 may have a different configuration or arrangementof the components depicted in FIG. 20 . The various components shown inFIG. 20 may be implemented in hardware, software, or a combination ofboth hardware and software, including one or more signal processingand/or application specific integrated circuits.

Further, the steps in the processing methods described herein may beimplemented by running one or more functional modules in informationprocessing apparatus such as general purpose processors or applicationspecific chips, such as ASICs, FPGAs, PLDs, or other appropriatedevices. These modules, combinations of these modules, and/or theircombination with general hardware are included within the scope of thepresent disclosure.

Computational interpretations, models, and/or other interpretation aidsmay be refined in an iterative fashion; this concept is applicable tothe methods discussed herein. This may include use of feedback loopsexecuted on an algorithmic basis, such as at a computing device (e.g.,computing system 2000, FIG. 20 ), and/or through manual control by auser who may make determinations regarding whether a given step, action,template, model, or set of curves has become sufficiently accurate forthe evaluation of the subsurface three-dimensional geologic formationunder consideration.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive orlimiting to the precise forms disclosed. Many modifications andvariations are possible in view of the above teachings. Moreover, theorder in which the elements of the methods described herein areillustrated and described may be re-arranged, and/or two or moreelements may occur simultaneously. The embodiments were chosen anddescribed in order to best explain the principles of the disclosure andits practical applications, to thereby enable others skilled in the artto best utilize the disclosed embodiments and various embodiments withvarious modifications as are suited to the particular use contemplated.

What is claimed is:
 1. A method for determining a total torque output ata drill bit, the method comprising: receiving an on-bottom pressure andan off-bottom pressure; determining a differential pressure based uponthe on-bottom pressure and the off-bottom pressure; receiving a surfacetorque; determining a torque transmission coefficient based at leastpartially upon the differential pressure and the surface torque; anddetermining the total torque output at the drill bit based at leastpartially upon the differential pressure, the surface torque, and thetorque transmission coefficient.
 2. The method of claim 1, wherein theon-bottom pressure and the off-bottom pressure are measured by apressure sensor at a surface above a wellbore, wherein the on-bottompressure comprises a pressure when a bottom hole assembly (BHA) is on abottom of the wellbore, and wherein the off-bottom pressure comprisesthe pressure when the BHA is off of the bottom of the wellbore.
 3. Themethod of claim 1, wherein the surface torque is measured by a torquesensor, wherein the torque sensor is coupled to a top drive, wherein thesurface torque comprises a torque introduced to a drill string by thetop drive, wherein the drill string extends into a wellbore, wherein abottom hole assembly (BHA) is coupled to a lower end of the drillstring, and wherein the BHA comprises a mud motor and the drill bit. 4.The method of claim 1, wherein the torque transmission coefficient is apositive unitless coefficient that is less than 1 and represents atorque transmission between stator rubber and a rotor in a mud motor. 5.The method of claim 1, wherein determining the torque transmissioncoefficient comprises: receiving a torque below a mud motor; multiplyinga torque slope of the mud motor and the differential pressure to producea first value; subtracting the first value from the torque below the mudmotor to produce a second value; and dividing the second value by thesurface torque to produce the torque transmission coefficient.
 6. Themethod of claim 1, wherein the torque transmission coefficient is alsodetermined based at least partially upon a temperature in a wellbore, apressure in the wellbore, a rate of rotation of a drill string in thewellbore, a weight on the drill bit in the wellbore, and a flow rate ofa fluid pumped into the wellbore.
 7. The method of claim 1, whereindetermining the total torque output comprises: multiplying a torqueslope of a mud motor and the differential pressure to produce a firstvalue; multiplying the surface torque and the torque transmissioncoefficient to produce a second value; and adding the first value andthe second value to produce the total torque output.
 8. The method ofclaim 1, further comprising displaying the total torque output.
 9. Themethod of claim 1, further comprising performing a wellsite action inresponse to the total torque output.
 10. The method of claim 9, whereinthe wellsite action comprises varying the on-bottom pressure, varyingthe off-bottom pressure, varying an amount of torque introduced into adrill string, varying a rate of rotation of the drill string, varying aweight on the drill bit, varying a toolface setting of a bottom holeassembly (BHA), varying a flow rate of a fluid being pumped into awellbore, or a combination thereof.
 11. A computing system, comprising:at least one processor; and a storage medium connected to the at leastone processor, the storage medium including instructions for configuringthe computing system to perform operations comprising: receiving anon-bottom pressure and an off-bottom pressure that are measured by apressure sensor, wherein the pressure sensor is at a surface above awellbore, wherein the on-bottom pressure comprises a pressure when abottom hole assembly (BHA) is on a bottom of the wellbore, and whereinthe off-bottom pressure comprises the pressure when the BHA is off ofthe bottom of the wellbore; determining a differential pressurecomprising a difference between the on-bottom pressure and theoff-bottom pressure; receiving a surface torque measured by a torquesensor, wherein the surface torque comprises a torque introduced to adrill string by a top drive, wherein the torque sensor is coupled to thetop drive, wherein the drill string extends into the wellbore, whereinthe BHA is coupled to a lower end of the drill string, and wherein theBHA comprises a mud motor and a drill bit; determining a torquetransmission coefficient based at least partially upon the differentialpressure and the surface torque, wherein the torque transmissioncoefficient is a positive unitless coefficient that is less than 1 andrepresents a torque between a rotor and stator rubber in the mud motor;and determining a total torque output at the drill bit based at leastpartially upon the differential pressure, the surface torque, and thetorque transmission coefficient.
 12. The computing system of claim 11,wherein the operations further comprise determining that performance ofthe mud motor is degrading in response to the total torque outputdeviating from an expected torque output by more than a predeterminedtorque threshold.
 13. The computing system of claim 11, wherein theoperations further comprise determining that the drill string is slidingin the wellbore in response to the total torque output being less than apredetermined torque threshold.
 14. The computing system of claim 11,wherein the operations further comprise determining that the drillstring is rotating in the wellbore in response to the total torqueoutput being greater than a predetermined torque threshold.
 15. Thecomputing system of claim 11, wherein determining the total torqueoutput comprises: multiplying a torque slope of the mud motor and thedifferential pressure to produce a first value; multiplying the surfacetorque and the torque transmission coefficient to produce a secondvalue; and adding the first value and the second value to produce thetotal torque output.
 16. A non-transitory machine-readable storagemedium having instructions stored thereon to configure a processor of acomputing system to perform operations, the operations comprise:receiving an on-bottom pressure and an off-bottom pressure that aremeasured by a pressure sensor, wherein the pressure sensor is at asurface above a wellbore, wherein the on-bottom pressure comprises apressure when a bottom hole assembly (BHA) is on a bottom of thewellbore, and wherein the off-bottom pressure comprises the pressurewhen the BHA is off of the bottom of the wellbore; determining adifferential pressure comprising a difference between the on-bottompressure and the off-bottom pressure; receiving a surface torquemeasured by a torque sensor, wherein the surface torque comprises atorque introduced to a drill string by a top drive, wherein the torquesensor is coupled to the top drive, wherein the drill string extendsinto the wellbore, wherein the BHA is coupled to a lower end of thedrill string, and wherein the BHA comprises a mud motor and a drill bit;determining a torque transmission coefficient based at least partiallyupon the differential pressure and the surface torque, wherein thetorque transmission coefficient is a positive unitless coefficient thatis less than 1 and represents a torque between a rotor and stator rubberin the mud motor; determining a total torque output at the drill bitbased at least partially upon the differential pressure, the surfacetorque, and the torque transmission coefficient, wherein the totaltorque output is determined by a model, and wherein determining thetotal torque output comprises: multiplying a torque slope of the mudmotor and the differential pressure to produce a first value;multiplying the surface torque and the torque transmission coefficientto produce a second value; and adding the first value and the secondvalue to produce the total torque output; and generating a signal inresponse to the total torque output, wherein the signal causes one ormore parameters to vary, and wherein the one or more parameters comprisethe on-bottom pressure, the off-bottom pressure, an amount of the torqueintroduced into the drill string by the top drive, a weight on the drillbit, a rate of rotation of the drill string, the BHA, or both, atoolface setting of the BHA, a flow rate of a fluid being pumped intothe wellbore, or a combination thereof.
 17. The non-transitorymachine-readable storage medium of claim 16, wherein determining thetorque transmission coefficient comprises: receiving a torque below themud motor; multiplying the torque slope of the mud motor and thedifferential pressure to produce a third value; subtracting the thirdvalue from the torque below the mud motor to produce a fourth value; anddividing the fourth value by the surface torque to produce the torquetransmission coefficient.
 18. The non-transitory machine-readablestorage medium of claim 16, wherein the torque transmission coefficientis determined also based at least partially upon a temperature in thewellbore, a pressure in the wellbore, a rate of rotation of the drillstring or the BHA in the wellbore, a weight on the drill bit in thewellbore, and the flow rate of the fluid pumped into the wellbore, andwherein the torque transmission coefficient is determined usingartificial intelligence (AI), machine-learning (ML), or both.
 19. Thenon-transitory machine-readable storage medium of claim 16, wherein theoperations further comprise determining that the BHA has encountered anabnormal pressure event at least partially in response to the torquetransmission coefficient, the total torque output, or both, and whereindetermining that the BHA has encountered the abnormal pressure eventcomprises: measuring a first standpipe pressure (SPP) at the surface;determining a second SPP at the surface; and determining that the firstSPP differs from the second SPP by more than a predetermined pressure.20. The non-transitory machine-readable storage medium of claim 19,wherein determining the second SPP comprises: multiplying a firstconstant and the flow rate squared to produce a first SPP value;multiplying a second constant, the flow rate squared, and a depth of thedrill bit to produce a second SPP value; multiplying a third constantand the total torque output to produce a third SPP value; multiplying afourth constant and the weight on the drill bit to produce a fourth SPPvalue; and adding the first SPP value, the second SPP value, the thirdSPP value, the fourth SPP value, and a fifth constant to produce thesecond SPP, wherein the first, second, third, fourth, and fifthconstants are different.